# Thread: Why is 2x^2-xy-3y^2 = (2x - 3y)(x + y) ?

1. ## Why is 2x^2-xy-3y^2 = (2x - 3y)(x + y) ?

Why is 2x^2-xy-3y^2 = (2x - 3y)(x + y) ? What kind of factorization is used here?

2. ## Re: Why is 2x^2-xy-3y^2 = (2x - 3y)(x + y) ?

It looks like a factorisation by grouping...

\displaystyle \begin{align*} 2x^2 - xy - 3y^2 &= 2x^2 - 3xy + 2xy - 3y^2 \\ &= x(2x - 3y) + y(2x - 3y) \\ &= (2x - 3y)(x + y) \end{align*}